The coefficient of x3y in (x - 2y) x (5x + y)3 is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. -175
(a + b)3 = a + 3a2b + 3ab2 + b3
(x - 2y) × (5x + y)3
⇒ (x - 2y) × (125x3 + 75x2y + 15xy2 + y3)
⇒ 125x4 + 75x3y + 15x2y2 + xy3 - 250x3y - 150x2y2 - 30xy3 - 2y4
⇒ 125x4 + (75x3y - 250x3y) + 15x2y2 + xy3- 150x2y2 - 30xy3 - 2y4
⇒ 125x4 + (-175x3y) + 15x2y2 + xy3- 150x2y2 - 30xy3 - 2y4
∴ The coefficient of x3y is (-175).